Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space: Apparent Behavior of Clocks

摘要

Coordinate transformations are derived from global Minkowski coordinates tothe Fermi coordinates of an observer moving in a circle in Minkowskispace-time. The metric for the Fermi coordinates is calculated directly fromthe tensor transformation rule. The behavior of ideal clocks is examined fromthe observer's reference frame using the Fermi coordinates. A complicatedrelation exists between Fermi coordinate time and proper time on stationaryclocks (in the Fermi frame) and between proper time on satellite clocks thatorbit the observer. An orbital Sagnac-like effect exists for portable clocksthat orbit the Fermi coordinate origin. The coordinate speed of light isisotropic but varies with Fermi coordinate position and time. The magnitudes ofthese kinematic effects are computed for parameters that are relevant to theGlobal Positioning System (GPS) and are found to be small; however, for futurehigh-accuracy time transfer systems, these effects may be of significantmagnitude.